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aencabo
This is answered by: https://brainly.com/question/2533949

Let's supose that your object is the orange rectangle rotating around the blue circle (see picture attached)
r = 1.0 [m] is the radius of the circle (it's R in your problem).ω [rad/s] - is the angular velocity of the object, it is measured in radians per second. We will compute it from the data you havev [m/s] - is the tangential/linear speed, it is measured in meters per second
We know that the rotational speed is 10 revolutions per 4 seconds.
10/4 rev/s = 2.5 rev/s
We convert rev/s in rad/s and we get:2.5 rev/s = 15.708 rad/s
So we found our angular speed: ω = 15.708 rad/s
The relationship between v and ω is:
v = ω · r = 15.708 · 1 = 15.708 m/s 
 Answer: the magnitude of the velocity around the circle is 15.708 m/s

valeriagonzalez0213

Answer:

[tex]a_{c}[/tex] = 246.49 m/s²

Explanation:

We apply the equations of uniform circular motion :

ω= θ/t   Formula (1)

[tex]a_{c}[/tex] = ω²*R  Formula (2)

Where:

θ : angle that the object travels (rad)

ω: angular velocity ( rad/s)

t : time (s)

[tex]a_{c}[/tex] : centripetal acceleration (m/s²)

R: radius (m)

Equivalence

1  revolution = 2π radianes =2π rad

Data

θ = ten revolutions =  10* 2π rad = 20π rad

t = 4.0 seconds = 4 s

R = 1.0 meter = 1 m

Problem development

We replace data in  Formula (1)  to calculate ω:

ω = 20π rad / 4 s

ω = 20π rad / 4 s = 15.7 rad / s

We replace data in  Formula (1)  to calculate the centripetal acceleration [tex]a_{c}[/tex] ;

[tex]a_{c}[/tex] = ( 15.7 rad /s )² * 1 m

[tex]a_{c}[/tex] = 246.49 m/s²

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